Hydraulic fracturing (also known as hydrofracturing, hydrofracking, or fracking) is a well known well-stimulation technique. The rock of a subterranean earth formation is fractured by a hydraulically pressurized fluid that typically includes water. The fluid may also include sand, other proppants (e.g., aluminum oxide), and/or chemicals. The fluid is injected into a wellbore at high pressure to create cracks in the deep-rock formations through which hydrocarbons can more freely flow. When the hydraulic pressure is removed from the well, small grains of proppant hold the fractures open. Recently, efforts have been made to model hydraulic fractures.
In an anisotropic formation, shear waves travel at different velocities with different propagating directions and polarizations. In borehole acoustic logging, the receivers are placed along the borehole axis so that only the wave traveling along the borehole axis is measured. Borehole acoustic logging can measure the shear wave anisotropy with different polarizations around the borehole which is sometimes referred to as the azimuthal anisotropy.
In most cases, an anisotropic rock can be modeled as a transverse isotropic (TI) material. For example, layered structures such as the structure of shale or layered fractures inside a rock can cause such anisotropy, which is sometimes referred to as intrinsic anisotropy. This material has one symmetry axis of infinite-fold rotational symmetry that is perpendicular to the layers. When the rock's symmetry axis is parallel to the borehole axis, there will be no observable shear wave anisotropy from acoustic logging since the shear modes propagating along the axis for this geometry have the same velocity regardless of the direction of polarization. This kind of configuration related to the borehole is sometimes referred to as vertically transverse isotropy (VTI).
If there is an angle between the symmetry axis and the borehole axis, the measured shear modes have two phase velocities corresponding to fast and slow modes with perpendicular polarization directions. In borehole dipole acoustic logging, azimuthal anisotropy may be observed when dipole modes are excited at different azimuthal directions. The configuration in which the rock's symmetry axis is perpendicular to the borehole axis is sometimes referred to as horizontally transverse isotropy (HTI). For HTI, the shear mode that is polarized along the fracture (or layer) direction has a faster velocity than the shear mode polarized perpendicular to the fractures.
Azimuthal anisotropy may also be induced by stress in earth formations. Before a borehole is drilled, the rock itself may be pre-stressed. Stress can change the rock's elastic properties so that the shear wave polarized along the largest principal stress may have a different shear velocity than shear waves polarized perpendicular to the largest principal stress. This kind of anisotropy has a different character than the intrinsic anisotropy in borehole acoustic logging. The stress will redistribute around the borehole after the well is drilled, so that the stress distribution (both its magnitude and direction) near the borehole may be very different from that far away from the borehole. The latter is considered to have the same stress condition as before the borehole is drilled. This stress re-distribution may cause the shear velocity to vary in both azimuthal and radial directions. A formation with intrinsic anisotropy is homogeneous around the borehole area, but the stress-induced anisotropy in such a medium is non-uniform.